Although mental rotation is one of the most studied topics in visual cognition, we still know little about how our visual system constructs a rotated view. One fundamental unanswered question surrounds the capacity of this rotation operation - how much visual information can we transform at once? Past work has tested relatively complex objects, likely rotated across complex multi-step operations, making it difficult to isolate the capacity of any individual step. Meanwhile, work using simpler displays (e.g. colored squares) in the selective tracking and visual memory literatures has made capacity estimates more measurable. We predicted that if a mental rotation task were similarly simplified, we could for the first time obtain capacity estimates for this task. Participants stored a multi-feature object (a pinwheel with four distinctly colored 'petals') in memory. Capacity for detecting feature swaps was similar to past estimates for this type of change, around 2 feature-part bindings. But when the task was altered to require mental rotation of the object to a depicted degree, capacity plummeted to just 1. But which one? We hypothesized that people chose one part of an object to act as the gauge for rotation magnitude (the 'needle' of the 'protractor'), and would remember only the feature of that part. Eyetracking revealed that people systematically guided their gaze along the imagined track of the top petal. The degree to which they followed this strategy had a strikingly large impact on their performance on the task, predicting more than 30% of the variance in individual differences. Furthermore, changes to this top part accounted for almost all noticed changes - swaps involving the non-tracked part were noticed at chance levels. Mental rotation can be a deeply capacity-limited operation, potentially limited to rotation of only a single part of an object at a time.